Mathematics 9709 · AS & A Level · Energy, work and power

Energy, work and power — practice question

A plane makes an angle of $\sin^{-1}\!\left(\tfrac{1}{8}\right)$ with the horizontal. $A$ and $B$ are two points on the same line of steepest descent, with $A$ lying above $B$. The length $AB$ is $12\,\text{m}$. A small object $P$ of mass $8\,\text{kg}$ is released from rest at $A$ and slides down the plane, reaching $B$ with speed $4.5\,\text{m s}^{-1}$. For the motion of $P$ from $A$ to $B$, determine
(i)[3]

the gain in kinetic energy of $P$ and the reduction in potential energy of $P$

(ii)[2]

the size of the constant resisting force acting opposite to the motion of $P$

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct evaluation of kinetic energy gain $= \frac{1}{2}mv^2 = 81\ \text{J}$

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